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Question Number 120614 by TANMAY PANACEA last updated on 01/Nov/20

Trigonometry

$${Trigonometry}\: \\ $$

Commented by TANMAY PANACEA last updated on 01/Nov/20

Commented by TANMAY PANACEA last updated on 01/Nov/20

Commented by TANMAY PANACEA last updated on 01/Nov/20

Commented by TANMAY PANACEA last updated on 01/Nov/20

Commented by Dwaipayan Shikari last updated on 01/Nov/20

tan(π/9)+4sin(π/9)  =(1/(cos20°))(sin20°+4cos20sin20°)  =(1/(cos20°))(sin20°+2sin40°)  =(1/(cos20°))(2sin30°cos10°+sin40°)  =(1/(cos20°))(sin80°+sin40°)  =(1/(cos20°))(2sin60°cos20°)  =(√3)

$${tan}\frac{\pi}{\mathrm{9}}+\mathrm{4}{sin}\frac{\pi}{\mathrm{9}} \\ $$$$=\frac{\mathrm{1}}{{cos}\mathrm{20}°}\left({sin}\mathrm{20}°+\mathrm{4}{cos}\mathrm{20}{sin}\mathrm{20}°\right) \\ $$$$=\frac{\mathrm{1}}{{cos}\mathrm{20}°}\left({sin}\mathrm{20}°+\mathrm{2}{sin}\mathrm{40}°\right) \\ $$$$=\frac{\mathrm{1}}{{cos}\mathrm{20}°}\left(\mathrm{2}{sin}\mathrm{30}°{cos}\mathrm{10}°+{sin}\mathrm{40}°\right) \\ $$$$=\frac{\mathrm{1}}{{cos}\mathrm{20}°}\left({sin}\mathrm{80}°+{sin}\mathrm{40}°\right) \\ $$$$=\frac{\mathrm{1}}{{cos}\mathrm{20}°}\left(\mathrm{2}{sin}\mathrm{60}°{cos}\mathrm{20}°\right) \\ $$$$=\sqrt{\mathrm{3}} \\ $$

Commented by Dwaipayan Shikari last updated on 01/Nov/20

tan(((2π)/9))−4sin(((2π)/9))  =(1/(cos40°))(sin40°−4sin40°cos40°  =(1/(cos40°))(sin40°−2sin80°)  =−(1/(cos40°))(2cos60°sin20°+sin80°)  =−(1/(cos40°))(2sin50cos30)  =−(√3)

$${tan}\left(\frac{\mathrm{2}\pi}{\mathrm{9}}\right)−\mathrm{4}{sin}\left(\frac{\mathrm{2}\pi}{\mathrm{9}}\right) \\ $$$$=\frac{\mathrm{1}}{{cos}\mathrm{40}°}\left({sin}\mathrm{40}°−\mathrm{4}{sin}\mathrm{40}°{cos}\mathrm{40}°\right. \\ $$$$=\frac{\mathrm{1}}{{cos}\mathrm{40}°}\left({sin}\mathrm{40}°−\mathrm{2}{sin}\mathrm{80}°\right) \\ $$$$=−\frac{\mathrm{1}}{{cos}\mathrm{40}°}\left(\mathrm{2}{cos}\mathrm{60}°{sin}\mathrm{20}°+{sin}\mathrm{80}°\right) \\ $$$$=−\frac{\mathrm{1}}{{cos}\mathrm{40}°}\left(\mathrm{2}{sin}\mathrm{50}{cos}\mathrm{30}\right) \\ $$$$=−\sqrt{\mathrm{3}} \\ $$

Commented by TANMAY PANACEA last updated on 01/Nov/20

thank you

$${thank}\:{you} \\ $$

Commented by TANMAY PANACEA last updated on 01/Nov/20

thank you

$${thank}\:{you} \\ $$

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